First slide

Dynamics of rotational motion about fixed axis

Question

A body of M.I. of 3 kg-m² rotating with an angular speed of 2 rad/sec has the same KE as a mass of 12 kg moving with a speed of

Moderate

A

2 m/sec
B

1 m/sec
C

4 m/sec
D

8 m/sec

Solution

K.E. of rotating body $= \frac{1}{2} {Iω}^{2}$
K.E. of a mass moving with velocity $V = \frac{1}{2} {mv}^{2}$
$∴ \frac{1}{2} {mv}^{2} = \frac{1}{2} {Iω}^{2} or v = ω \sqrt{(I / m)}$
or $V = 2 \sqrt{(\frac{3}{12})} = 1 m / \sec$

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